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The mathematical study of knots. Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ...

A fractal derived from the Koch snowflake. The base curve and motif for the fractal are illustrated below. The area enclosed by pieces of the curve after the nth iteration is ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...

The Laplace distribution, also called the double exponential distribution, is the distribution of differences between two independent variates with identical exponential ...

A Laurent polynomial with coefficients in the field F is an algebraic object that is typically expressed in the form ...+a_(-n)t^(-n)+a_(-(n-1))t^(-(n-1))+... ...

Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. Then the law of sines states that a/(sinA)=b/(sinB)=c/(sinC)=2R, (1) where R is the ...

Let a triangle have sides of length a, b, and c and let the angles opposite these sides be denoted A, B, and C. The law of tangents states ...

A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points. The limiting points correspond to the point ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

For a logarithmic spiral given parametrically as x = ae^(bt)cost (1) y = ae^(bt)sint, (2) evolute is given by x_e = -abe^(bt)sint (3) y_e = abe^(bt)cost. (4) As first shown ...